TY - JOUR
T1 - Stochastic observability test for discrete-time kalman filters
AU - Bageshwar, Vibhor L.
AU - Gebre-Egziabher, Demoz
AU - Garrard, William L.
AU - Georgiou, Tryphon T.
N1 - Funding Information:
This work was partially supported by NASA under Minnesota Space Grant NNG05GG39H.
PY - 2009
Y1 - 2009
N2 - Stochastic observability refers to the existence of a filter for which the errors of the estimated state mean vector have bounded variance. In this paper, we derive a test to assess the stochastic observability of a Kalman filter implemented for discrete linear time-varying stochastic systems. This test is derived with the assumptions that the system matrices consist of known deterministic parameters and that there is complete uncertainty in the statistics of the initial state vector. This test can also be used to assess the stochastic observability of extended Kalman filters implemented for nonlinear stochastic systems linearized about the true state vector trajectory. We illustrate the utility of the stochastic observability test using an aided inertial navigation system.Wealso provide a counterexample to illustrate that observability is a necessary, but not sufficient, condition for the stochastic observability of a Kalman filter implemented for a system.
AB - Stochastic observability refers to the existence of a filter for which the errors of the estimated state mean vector have bounded variance. In this paper, we derive a test to assess the stochastic observability of a Kalman filter implemented for discrete linear time-varying stochastic systems. This test is derived with the assumptions that the system matrices consist of known deterministic parameters and that there is complete uncertainty in the statistics of the initial state vector. This test can also be used to assess the stochastic observability of extended Kalman filters implemented for nonlinear stochastic systems linearized about the true state vector trajectory. We illustrate the utility of the stochastic observability test using an aided inertial navigation system.Wealso provide a counterexample to illustrate that observability is a necessary, but not sufficient, condition for the stochastic observability of a Kalman filter implemented for a system.
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U2 - 10.2514/1.38128
DO - 10.2514/1.38128
M3 - Article
AN - SCOPUS:68049143185
SN - 0731-5090
VL - 32
SP - 1356
EP - 1370
JO - Journal of Guidance, Control, and Dynamics
JF - Journal of Guidance, Control, and Dynamics
IS - 4
ER -